Towards bulk metric reconstruction from extremal area variations

Ning Bao, Chunjun Cao, Sebastian Fischetti, Cynthia Keeler

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension d ≥ 4, knowledge of the (variations of the) areas of twodimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an explicit spacetime metric reconstruction.

Original languageEnglish (US)
Article number185002
JournalClassical and Quantum Gravity
Volume36
Issue number18
DOIs
StatePublished - 2019

Keywords

  • AdS/CFT
  • boundary rigidity
  • bulk reconstruction
  • holographic entanglement entropy

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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